NEW GAUGE INVARIANT FORMULATION OF THE CHERN–SIMONS GAUGE THEORY: CLASSICAL AND QUANTAL ANALYSIS

Author:

PARK MU-IN1,PARK YOUNG-JAI2

Affiliation:

1. Research Institute of Physics and Chemistry, Chonbuk National University, Chonju 561-756, Korea

2. Department of Physics and Center for Quantum Spacetime, BK21 Program Division, Sogang University, Seoul 121-742, Korea

Abstract

A recently proposed new gauge invariant formulation of the Chern–Simons gauge theory is considered in detail. This formulation is consistent with the gauge fixed formulation. Furthermore, it is found that the canonical (Noether) Poincaré generators are not gauge invariant even on the constraints surface and do not satisfy the Poincaré algebra contrast to usual case. It is the improved generators, constructed from the symmetric energy–momentum tensor, which are (manifestly) gauge invariant and obey the quantum as well as classical Poincaré algebra. The physical states are constructed and it is found in the Schrödinger picture that unusual gauge invariant longitudinal mode of the gauge field is crucial for constructing the physical wave-functional which is genuine to (pure) Chern–Simons theory. In matching to the gauge fixed formulation, we consider three typical gauges, Coulomb, axial and Weyl gauges as explicit examples. Furthermore, recent several confusions about the effect of Dirac's dressing function and the gauge fixings are clarified. The analysis according to old gauge independent formulation á la Dirac is summarized in an appendix.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Astronomy and Astrophysics,Nuclear and High Energy Physics,Atomic and Molecular Physics, and Optics

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